3.) Since RECT is a rectangle, the corners must be 90 degrees each. Angle ECT is one of the corners, o we can set 11x+13 equal to 90.
11x + 13 = 90
11x = 77
x= 7
4.) The diagonals of a rhombus are perpendicular meaning they form 90 degree angles. So set 14x+6 equal to 90.
14x + 6 = 90
14x = 84
x = 6
7.) The diagonals of a square also form 90 degree angles. Since all the sides of a sqaure are equal, we know that SQR and QSR must be equal. Since QRS is 90 and the angles of a triangle must add to 180, we know that SQR is 45.
4x + 1 = 45
4x = 44
x = 11
8.) Set it equal to 90 like the first two problems.
11x + 2 = 90
11x = 88
x = 8
9.) It looks like he got 9 right! The two sides are equal lengths, so they can be set equal to each other to solve for x.